Relation


Relation : Let A and B be two sets, then a relation R from A to B is a subset of A ×B.

Thus, R is a relation from A to B . ⇔  R ⊆ A × B

Recall that A × B is a set of all ordered pairs whose first member is from the set A and second member is from B i.e.,

  × B = {(x,y) : x  A and y ∈ B }

If R is a relation from a non-empty set A to a non-empty set B and if (a, b R, then we write aRb which is read as a is related to b by the relation R. If (a, b∉ R then we write   and we say that a is not related to b by the relation R. In other words, a relation is a set of inputs and outputs, often written as ordered pairs (input, output). We can also represent a relation as a mapping or a graph. For example, a relation can be represented as:

Mapping diagram of Relation

A relation can also be represented as: